Let T_0=2, T_1=3, T_2=6, and for n>=3, 

T_n=(n+4)T_(n-1)-4nT_(n-2)+(4n-8)T_(n-3).

The first few terms are 

2, 3, 6, 14, 40, 152, 784, 5168, 40576, 363392.

Find, with proof, a formula for T_n of the form T_n=A_n+B_n,

where (A_n) and (B_n) are well-known sequences.

[They don't give any further hint. But considering the ratio of consecutive

T_n's it seems likely that n! is somehow involved. Think about it.]